Processing Math: Done

From Förberedande kurs i matematik 1

For a fixed value of u, an equality of the form

cosu=cosv

is satisfied by two angles v in the unit circle,

v=uandv=−u.

This means that all angles v which satisfy the equality are

v=u+2nandv=−u+2n

where n is an arbitrary integer.

Therefore, the equation

cos5x=cos(x+5)

has the solutions

5x5x=x+5+2nor=−x−5+2n.

If we collect x onto one side, we end up with

xx=20+2n=−30+3n

where n is an arbitrary integer.